Time-Cycle or Schwinger-Keldysh Formulation

  • Kimball A. MiltonEmail author
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)


A further utility of the action principle is the time-cycle or Schwinger-Keldysh formalism, which allows one to calculate matrix elements and consider nonequilibrium systems. Schwinger’s original work on this was his famous paper (Schwinger 1961); Keldysh’s paper appeared three years later (Keldysh 1964), and, rather mysteriously, cites the Martin-Schwinger equilibrium paper (Martin 1959), but not the nonequilibrium one (Schwinger 1961). The following was extracted from notes from Schwinger’s lectures given in 1968 at Harvard, as taken by the author.

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© The Author(s) 2015

Authors and Affiliations

  1. 1.Homer L. Dodge Department of Physics and AstronomyThe University of OklahomaNormanUSA

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